From my experience, the mail-triggered command must 1st deliver the message to the mailbox then execute the command (with a copy of the message perhaps) for WordPress to read and post the messages.
I use procmail to run the command (with a copy recipe), and then deliver the message. This is not-quite-right though – it means that a message will only get published when I send another message, which will in turn get posted after I send a third message & so on…
The command I actually use something like ‘wget --spider https://[site]/wp-mail.php"
‘ to simulate viewing the page.
I haven’t had much experience with procmail, or .forward triggered commands and would also appreciate anyone’s input.